Details

sample72.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 50%

Guaranteed chance to sample good point: 47.04159%

Results

20.0ms	290×	body	80	nan
16.0ms	285×	body	80	valid

simplify92.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	10
1	72	10
2	192	10
3	437	10
4	816	10
5	1578	10
6	2764	10
7	5002	10

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.1b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.2b	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
0.3b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
26×	`*-un-lft-identity` `times-frac`
24×	`add-cube-cbrt` `associate-l`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
8×	`associate-*r/` `sqrt-prod`
6×	`flip3--` `sqrt-div` `associate-r` `flip--`
4×	`frac-times` `associate-/r*` `associate-/r/` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `associate-l/` `prod-exp` `cbrt-unprod` `flip-+` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `sqrt-pow1` `div-exp` `*-commutative` `div-inv` `difference-of-squares`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow1/2` `clear-num` `distribute-lft-out--`

Counts

4 → 114

Calls

4 calls:

10.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
13.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
9.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series50.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
5.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
19.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
12.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify102.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	1008	1422
1	4617	1341
2	5001	1341

prune356.0ms

Filtered

105 candidates to 126 candidates (-20.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	117	9	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	9	127

Merged error: 0b

Counts

127 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9.0 (- a (/ 1.0 3.0)))
0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.2b	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
10×	`add-cube-cbrt` `associate-r`
9×	`associate-l`
8×	`associate-*r/`
6×	`flip3--` `times-frac` `flip--`
4×	`frac-times` `sqrt-div` `associate-/r*` `add-log-exp` `difference-of-squares`
3×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod` `flip-+`
2×	`cbrt-undiv` `sub-neg` `sqrt-pow1` `div-exp` `associate-l/` `associate-/r/` `-commutative` `distribute-lft-out--` `unswap-sqr`
1×	`frac-2neg` `pow1/2` `clear-num` `div-inv` `distribute-lft-out` `associate-/l*`

Counts

4 → 97

Calls

4 calls:

10.0ms	(* 9.0 (- a (/ 1.0 3.0)))
13.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
11.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series39.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 9.0 (- a (/ 1.0 3.0)))
14.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
5.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
16.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify92.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	870	1101
1	4263	1027
2	5001	1027

prune239.0ms

Filtered

83 candidates to 109 candidates (-31.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	112	6	118

Merged error: 0b

Counts

118 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9.0 (- a (/ 1.0 3.0)))
0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.2b	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
7.5b	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`add-exp-log` `add-cbrt-cube`
16×	`associate-r`
15×	`*-un-lft-identity`
11×	`pow1` `add-cube-cbrt`
10×	`times-frac`
9×	`associate-r/` `associate-l*`
6×	`flip3--` `sqrt-div` `prod-exp` `flip--` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `associate-/r*` `sqrt-prod` `associate-/r/` `add-log-exp` `difference-of-squares`
3×	`pow-prod-down`
2×	`distribute-rgt-in` `frac-times` `sub-neg` `distribute-lft-in` `sqrt-pow1` `associate-l/` `-commutative` `div-inv` `distribute-lft-out--` `unswap-sqr`
1×	`frac-2neg` `pow1/2` `clear-num` `associate-/l*`

Counts

4 → 102

Calls

4 calls:

9.0ms	(* 9.0 (- a (/ 1.0 3.0)))
7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
11.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
20.0ms	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

series46.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 9.0 (- a (/ 1.0 3.0)))
5.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
16.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
21.0ms	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

simplify101.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	857	1103
1	4190	994
2	5002	994

prune246.0ms

Filtered

86 candidates to 114 candidates (-32.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	114	6	120

Merged error: 0b

Counts

120 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- a (/ 1.0 3.0))
0.0b	(sqrt (- a (/ 1.0 3.0)))
0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
0.3b	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

164×	`times-frac`
132×	`add-sqr-sqrt`
102×	`sqrt-prod`
89×	`*-un-lft-identity`
59×	`add-cube-cbrt`
28×	`difference-of-squares`
15×	`add-exp-log` `add-cbrt-cube`
14×	`distribute-lft-out--`
11×	`div-inv`
10×	`associate-/l*`
9×	`associate-/r*`
7×	`pow1`
6×	`flip3--` `associate-l` `flip--` `add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`frac-times` `sqrt-div` `associate-r`
3×	`flip3-+` `flip-+`
2×	`associate-r/` `associate-l/` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`distribute-rgt-in` `sub-neg` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `clear-num` `*-commutative` `associate-/l/` `distribute-lft-out` `unswap-sqr`

Counts

4 → 193

Calls

4 calls:

6.0ms	(- a (/ 1.0 3.0))
6.0ms	(sqrt (- a (/ 1.0 3.0)))
34.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
14.0ms	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

series40.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(- a (/ 1.0 3.0))
3.0ms	(sqrt (- a (/ 1.0 3.0)))
15.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
19.0ms	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

simplify52.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1119	2652
1	5001	2497

prune423.0ms

Filtered

132 candidates to 205 candidates (-55.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	204	1	205
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	206	5	211

Merged error: 0b

Counts

211 → 5

regimes140.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	13
1	19	13

end0.0ms

sample1.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 50%

Guaranteed chance to sample good point: 47.04159%

Results

539.0ms	9165×	body	80	valid
486.0ms	9070×	body	80	nan

Details

sample72.0ms

simplify92.0ms

prune3.0ms

localize10.0ms

rewrite43.0ms

series50.0ms

simplify102.0ms

prune356.0ms

localize11.0ms

rewrite44.0ms

series39.0ms

simplify92.0ms

prune239.0ms

localize13.0ms

rewrite50.0ms

series46.0ms

simplify101.0ms

prune246.0ms

localize14.0ms

rewrite71.0ms

series40.0ms

simplify52.0ms

prune423.0ms

regimes140.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.5s

Profiling